SOLUTION: This year, your brother Jack will be 2 years from being twice as old as your sister Jen. The sum of Jack's age and three times Jen's age is 66. How old is Jen?

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Question 214484: This year, your brother Jack will be 2 years from being twice as old as your sister Jen. The sum of Jack's age and three times Jen's age is 66. How old is Jen?
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
This year, your brother Jack will be 2 years from being twice as old as your sister Jen. The sum of Jack's age and three times Jen's age is 66. How old is Jen?

Step 1. Let x by Jen's age. Let 2x-2 be Jack's age (2 year from being twice as old as sister Jen)

Step 2. 2x-2+3x=66 (the sum of Jack's age and three times Jen's age is 66)

Step 3. The following steps will solve the above equation:

Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: x=13.6.
  • Graphical form: Equation 2x-2%2B3x=66 was fully solved.
  • Text form: 2x-2+3x=66 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+2x-2%2B3x=66+%29
    For tutors: simplify_cartoon( 2x-2+3x=66 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 2%2Ax-highlight_red%28+2+%29%2B3%2Ax=66.
Moved -2 to the right of expression
It becomes 2%2Ax%2B3%2Ax-highlight_green%28+2+%29=66.
Look at highlight_red%28+2%2Ax+%29%2Bhighlight_red%28+3%2Ax+%29-2=66.
Eliminated similar terms highlight_red%28+2%2Ax+%29,highlight_red%28+3%2Ax+%29 replacing them with highlight_green%28+%282%2B3%29%2Ax+%29
It becomes highlight_green%28+%282%2B3%29%2Ax+%29-2=66.
Look at %28highlight_red%28+2+%29%2Bhighlight_red%28+3+%29%29%2Ax-2=66.
Added fractions or integers together
It becomes %28highlight_green%28+5+%29%29%2Ax-2=66.
Look at highlight_red%28+%28highlight_red%28+5+%29%29%2Ax+%29-2=66.
Remove unneeded parentheses around factor highlight_red%28+5+%29
It becomes highlight_green%28+5+%29%2Ax-2=66.
Look at 5%2Ax-2=highlight_red%28+66+%29.
Moved these terms to the left highlight_green%28+-66+%29
It becomes 5%2Ax-2-highlight_green%28+66+%29=0.
Look at 5%2Ax-highlight_red%28+2+%29-highlight_red%28+66+%29=0.
Added fractions or integers together
It becomes 5%2Ax%2Bhighlight_green%28+-68+%29=0.
Look at 5%2Ax%2Bhighlight_red%28+-68+%29=0.
Removed extra sign in front of -68
It becomes 5%2Ax-highlight_green%28+68+%29=0.
Look at highlight_red%28+5%2Ax-68+%29=0.
Solved linear equation highlight_red%28+5%2Ax-68=0+%29 equivalent to 5*x-68 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=13.6.

Universal Simplifier and Solver


Done!



Step 4. The age of Jen is 13.6 years old.

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J